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5 - Theory of Minimum Variance

Published online by Cambridge University Press:  24 November 2022

Vijay P. Singh
Affiliation:
Texas A & M University
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Summary

The concept of minimum variance is a statistical concept, and its premise is that a river tends to minimize the variability of factors that govern its hydraulic geometry. This concept has been applied in different ways and this chapter discusses the theory of minimum variance from different viewpoints.

Type
Chapter
Information
Handbook of Hydraulic Geometry
Theories and Advances
, pp. 159 - 185
Publisher: Cambridge University Press
Print publication year: 2022

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References

Brush, L. M. (1961). Drainage basins, channels, and flow characteristics of selected streams in central Pennsylvania. U.S. Geological Survey Professional Paper 2 82-F, Washington, DC.CrossRefGoogle Scholar
Chorley, R. J. (1962). Geomorphology and general systems theory. Geological Professional Paper 500-B, U.S. Geological Survey, Washington, DC.Google Scholar
Colby, B. R. (1964). Discharge of sands and mean velocity relationships in sand-bed streams. Professional Paper 462 A, U.S. geological Survey, Washington, DC..CrossRefGoogle Scholar
Dozier, J. (1976). An examination of the variance minimization tendencies of a supraglacial stream. Journal of Hydrology, Vol. 31, pp. 359380.Google Scholar
Emmett, W. W. (1970). The hydraulics of overland flow on hillslopes. U.S. Geological Survey Professional Paper, 642-A, p. 68.Google Scholar
Gilbert, G. K. (1877). Report on the geology of the Henry Mountains. U.S. Geological Survey Rocky Mountain Region Report, pp. 160.CrossRefGoogle Scholar
Kennedy, J. F., Richardson, P. O., and Sutera, S. P. (1964). Discussion of “Geometry of river channels” by W. B Langbein. Proceedings of the Hydraulics Division, ASCE, Vol. 90, No. HY6, pp. 332341.Google Scholar
Knighton, A. D. (1972). Changes in a braided reach. Geological Society of America Bulletin, Vol. 83, pp. 38133822.CrossRefGoogle Scholar
Knighton, A. D. (1974). Variation in width-discharge relation and some implications for hydraulic geometry. Geological Society of America Bulletin, Vol. 85, pp. 10691076.2.0.CO;2>CrossRefGoogle Scholar
Knighton, A. D. (1975). Variations in at-a-station hydraulic geometry. American Journal of Science, Vol. 275, pp. 186218.CrossRefGoogle Scholar
Knighton, A. D. (1977). Alternative derivation of the minimum variance hypothesis. Geological Society of America Bulletin, Vol. 88, pp. 364366.2.0.CO;2>CrossRefGoogle Scholar
Langbein, W. B. (1964). Geometry of river channels. Journal of the Hydraulics Division, ASCE, Vol. 90, No. HY2, pp. 301311.CrossRefGoogle Scholar
Langbein, W. B. (1965). Closure to “Geometry of river channels.” Proceedings of the Hydraulics Division, ASCE, Vol. 91, No. HY3, pp. 297313.CrossRefGoogle Scholar
Langbein, W. B. and Leopold, L. B. (1966). River meanders-theory of minimum variance. U.S. Geological Survey Professional Paper 422-H, 15 pp., Washington, DC.CrossRefGoogle Scholar
Leopold, L. B. and Maddock, T. J. (1953). Hydraulic geometry of stream channels and some physiographic implications. U. S. Geological Survey Professional Paper, 252, p. 55.Google Scholar
Lindley, E. S. (1919). Regime Channels. Minutes and Proceedings, Punjab Engineering Congress, Lahore, 7.Google Scholar
Maddock, T. (1969). The behavior of straight open channels with movable beds. U.S. Geological Professional Paper, 622-A, pp. 70.Google Scholar
Richards, K. S. (1973). Hydraulic geometry and channel roughness: A nonlinear system. American Journal of Science, Vol. 273, pp. 877896.Google Scholar
Richards, K. S. (1976). Complex width-discharge relations in natural river sections. Geological Society of America Bulletin, Vol. 87, pp. 199206.2.0.CO;2>CrossRefGoogle Scholar
Richards, K. S. (1982). Rivers: Form and Process in Alluvial Channels. Metheun, London.Google Scholar
Riley, S. J. (1978). The role of minimum variance theory in defining the regime characteritics of the Lower Namgoi-Gwydir drainage basin. Water Resources Bulletin, Vol. 14, No. 1, pp. 111.Google Scholar
Rubey, W. W. (1953). Geology and mineral resources of the Hardin and Brussels quadrangles. Professional Paper 218, pp. 175, U.S. Geological Survey, Washington, DC.Google Scholar
Williams, G. P. (1978). Hydraulic geometry of river cross-sections-Theory of minimum variance. U.S. Geological Survey Professional Paper 1029, Washington, DC.Google Scholar

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